Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session AM: Flows in Porous Media |
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Chair: Yiannis Andreopoulis, City University of New York Room: Hilton Chicago PDR 1 |
Sunday, November 20, 2005 8:00AM - 8:13AM |
AM.00001: Averaging non-slender gravity currents in heterogeneous porous media Daniel Anderson, Richard McLaughlin, Casey Miller We explore the slumping of a gravity current in a water-saturated porous medium whose permeability field is periodically heterogeneous. We focus on the non-slender regime in which the height of the gravity current is not necessarily much smaller than its width. Our formulation uses a sharp moving interface that defines the slumping region. We discuss details of how this nonlinear moving interface problem is homogenized with respect to rapidly-varying permeability fields. In this fully two-dimensional setting, we compare numerical computations for the heterogeneous permeability field with computations using a constant effective permeability matrix derived from leading-order homogenization theory. We discuss the connection of this formulation with one which tracks a miscible fluid region without a sharp moving boundary. Finally, we comment on the possibility of incorporating corrections to the leading-order homogenization results. [Preview Abstract] |
Sunday, November 20, 2005 8:13AM - 8:26AM |
AM.00002: Onset of convection in a gravitationally unstable diffusive boundary layer, in a porous medium Marc Hesse, Amir Riaz, Hamdi Tchelepi, Lynn Orr, Jr. We present a linear stability analysis of density driven, miscible flow in porous media in the context of CO$_{2}$ sequestration in saline aquifers. CO$_{2}$ dissolution into the underlying brine leads to a local density increase that results in a gravitational instability. The physical phenomenon is analogous to the thermal convective instability in a semi-infinite domain, due to step change in temperature at the boundary. We present a solution, based on the dominant mode of the self-similar diffusion operator, which can accurately predict the critical time and the associated unstable wavenumber. This approach is used to explain the instability mechanisms of the critical time and the longwave cutoff in a semi-infinite domain. For large times, both the maximum growth rate and the most dangerous mode decay as $t^{1/4}$ . The instability problem is also analyzed in the nonlinear regime by high accuracy direct numerical simulations. The nonlinear simulations at short times show good agreement with the linear stability predictions. A dimensional analysis for typical aquifers shows that for a permeability variation of 1 - 3000 mD, the critical time can vary from 2000 yrs to about 10 days while the critical wavelength can be between 200m and 0.3 m. [Preview Abstract] |
Sunday, November 20, 2005 8:26AM - 8:39AM |
AM.00003: Linear stability analysis of immiscible two-phase flow in porous media Amir Riaz, Hamdi Tchelepi Linear stability analysis of immiscible displacements is carried out for both viscously and gravitationally unstable two-phase flows in porous media with very large adverse viscosity ratios. Capillary dispersion is the proper dissipative mechanism in this case which sets both the preferred length scale and the band width of the spectrum of unstable length scales. The growth rate, the most dangerous and the cutoff wavenumbers, all scale linearly with the capillary number. We show that the instability is governed by fluid properties across the shock rather than those across the full Buckley--Leverett profile. The shock total mobility ratio provides a sufficient condition for the onset of instability; however, it is not an appropriate criterion for predicting the magnitude of the growth rate, particularly for large viscosity ratios. The details of the relative permeability functions are observed to have a significant influence on the stability characteristics. For neutrally buoyant flows the maximum growth rate scales linearly with the viscosity ratio while the most dangerous and the cutoff wavenumbers scale with the square root of the viscosity ratio. [Preview Abstract] |
Sunday, November 20, 2005 8:39AM - 8:52AM |
AM.00004: On the Selection Principle for Viscous Fingering in Porous Media Yannis C. Yortsos, Dominique Salin Viscous fingering in porous media at large Peclet numbers is subject to an unsolved selection problem, not unlike the Saffman-Taylor problem. The mixing zone predicted by the entropy solution of the resulting hyperbolic problem, is found to spread much faster than what is observed experimentally or by fine-scale numerical simulations. In this paper we apply a recent approach by Menon and Otto (Com. Math. Phys, {\bf 257}, 303-317, (2005)) to develop bounds in the growth of the mixing zone. These predict growth velocities smaller than what is obtained by the entropy solution. For an exponential viscosity- concentration mixing rule, the mixing zone velocity is shown to be bounded by $\frac{(M-1) ^2}{M{\rm ln}M}$ which is significantly smaller than the entropy solution result $\left(M- \frac{1}{M}\right)$. [Preview Abstract] |
Sunday, November 20, 2005 8:52AM - 9:05AM |
AM.00005: Fingering Instabilities in a Granular Hele-Shaw Cell Xiang Cheng, Aaron Patterson, Lei Xu, Heinrich Jaeger, Sidney Nagel In many respects, dry granular material can be thought of as a fluid with no surface tension. We have used this ``liquid'' to study the fingering instability that occurs in a Hele-Shaw cell in which air entering at the center of a 2-dimensional cell displaces the surrounding dry granular material which is held between two closely spaced glass plates. This provides a situation in which one can study fingering in the limit of zero surface tension. We have systematically studied the fractal dimension of the fingering pattern during the growth process. The final pattern that we observe has a shape with a fractal dimension close to 1.7. We also study the dependence of the fingers on the flux rate, size of grains and size of gap between the glass plates. The mechanisms for the instabilities are investigated. [Preview Abstract] |
Sunday, November 20, 2005 9:05AM - 9:18AM |
AM.00006: Reaction characteristics of reactive miscible viscous fingering of water soluble polymer solution in a Hele-Shaw cell Yuji Hosokawa, Yuichiro Nagatsu, Yoshihito Kato, Yutaka Tada Reactive miscible viscous fingering occurs when a reactive and miscible less-viscous liquid displaces a more-viscous liquid in a Hele-Shaw cell. In the present study, to investigate the effect of polymeric characteristics of liquid on this issue, we experimentally compared reactive miscible viscous fingering in a Hele-Shaw cell formed in a water-soluble polymer solution with that formed in a glycerin solution having the almost same viscosity as the water-soluble polymer solution has. Under the present experimental condition, product distributions in the fingering formed in the glycerin solution depends on the ratio between initial reactant concentrations included in the more- and less-viscous liquids normalized by the stoichiometric ratio of the chemical reaction, $\phi$$_{v}$; the product significantly exists inside the fingers for $\phi$$_{v} $$<$$<$1, while it concentrates around the fingertips for $\phi$$_{v} $$>$$>$1. On the other hand, product distributions in the fingering formed in the water-soluble polymer are independent of $\phi$$_{v}$ [Preview Abstract] |
Sunday, November 20, 2005 9:18AM - 9:31AM |
AM.00007: Influence of the Joule-Thomson effect on the flow of a vapor through a micro-porous membrane Thomas Loimer The flow of a fluid near saturation through a micro-porous membrane is considered. Upstream of the membrane, the fluid is in a state of saturated vapor. Downstreams, there is unsaturated vapor which is, due to the Joule-Thomson effect, cooler than at the upstream side. The flow is described taking into account the Joule-Thomson effect and the wetting properties between the fluid and the membrane material, i.e., the capillary pressure across a curved meniscus and capillary condensation. Different types of flow occur, depending on the permeability of the membrane, on the wetting properties between the fluid and the membrane and on the pressure difference. The fluid condenses either fully or partially at the front surface of the membrane, or a liquid film forms in front of the membrane. Liquid or a two-phase mixture flows through a part or all of the membrane and evaporates either within the membrane or at the downstream front of the membrane, or the fluid evaporates at the upstream front of the membrane and vapor flows through the entire membrane. The different types of flow are discussed and the conditions under which they occur are presented. [Preview Abstract] |
Sunday, November 20, 2005 9:31AM - 9:44AM |
AM.00008: Numerical evaluation of thermal dispersion in porous media May-Fun Liou, Isaac Greber The term ``thermal dispersion'' is used to refer the thermal transport enhancement occurring when fluid undergoes mixing as it traverses the tortuous paths around the solid phase in a porous medium. The effect of the resulting hydrodynamic mixing can be high compared with the molecular diffusion at high Reynolds numbers, especially when the heat conductivity of the solid phase in a porous medium is low. A previously described numerical method (APS/DFD 56, 57) for directly simulating flow over micro-structured porous media by solving the coupled three dimensional Navier-Stokes and heat conduction equations is applied within the porous fluid-solid system. The method does not require any imposed thermal dispersion model; the dispersion effects are be directly calculated at pore scale, without any additional interfacial conduction condition between solid and solid phases. The numerically obtained thermal dispersion conductivity tensor, which represents the heat transfer caused by hydrodynamic mixing of the interstitial fluid, is examined at various Reynolds numbers or Peclet numbers. [Preview Abstract] |
Sunday, November 20, 2005 9:44AM - 9:57AM |
AM.00009: Renormalized Numerical Simulation of Flow in Fractal Porous Media Saikiran Rapaka, Charles Meneveau, Shiyi Chen We present a new technique for modeling flow in fractal porous media using the idea of downscaling, as opposed to traditional upscaling. Only the large scale features of the domain are resolved and the information from the simulation of large scales is used to compute contributions from the smaller scales. The procedure is carried out iteratively, adding finer scales at every iteration. The permeability field is updated at every iteration based on information about the geometry of the finer scales. This method allows us to compute effective permeabilities for complex geometries without the need to resolve numerically the fine scales. The results of this approach are compared to full simulations for a set of simple fractal structures with different porosities. It is shown this method gives a high accuracy for these systems. We also compare the final permeability fields to those obtained from traditional upscaling methods. [Preview Abstract] |
Sunday, November 20, 2005 9:57AM - 10:10AM |
AM.00010: Effect of superfluid to normal component transition on the flow of He II in confined geometries Howard Snyder When He II flows up a thermal gradient the transition of the superfluid component to the normal component causes several effects. The velocities of the superfluid and normal components vary with distance even when the area of the flow path is constant. The temperature, pressure and chemical potential may have maxima on the profiles along the flow channel. These effects are proportional to the length of the channel divided by the mean square of the diameter. Flow in a tube with diameter smaller than 10 microns and longer than about 1 cm has deviations from the constant property solutions that are significant. We present a method to include the superfluid transition in the analysis of flow through confined passages such as capillaries and porous materials. It uses a step function approach with convolution, similar to the Green's function formalism. The method is iterative on the pressure and temperature profiles. We formulate the method so that the transition effects are an additive series to the constant property solutions with each iteration adding a term. We derive analytic formulas for the terms of the series. We apply the formulas to flows through confined passages with particular attention to changes in the critical velocity for the onset of superfluid turbulence. [Preview Abstract] |
Sunday, November 20, 2005 10:10AM - 10:23AM |
AM.00011: Lift mechanics of downhill skiing and snowboarding Qianhong Wu, Yesim Igci, Yiannis Andreopoulos, Sheldon Weinbaum A simplified mathematical model is derived to describe the lift mechanics of downhill skiing and snowboarding, where the lift contributions due to both the transiently trapped air and the compressed snow crystals are determined for the first time. Using Shimizu's empirical relation to predict the local variation in snow permeability, we employ force and moment analysis to predict the angle of attack of the planing surface, the penetration depth at the leading edge and the shift in the center of pressure for two typical snow types, fresh and wind-packed snow. We present numerical solutions for snowboarding and asymptotic analytic solutions for skiing for the case where there are no edging or turning maneuvers, which shows that approximately 50{\%} of the total lift force is generated by the trapped air in the case of wind-packed snow for snowboarding and 40{\%} for skiing. For highly permeable fresh powder snow the lift contribution from the pore air pressure drops to $<$ 20{\%}. This new theory is an extension of the series of studies on lift generation in highly compressible porous media. [Preview Abstract] |
Sunday, November 20, 2005 10:23AM - 10:36AM |
AM.00012: WITHDRAWN: Solving the inverse problem of tracer fluw using a hybrid optimization method Oscar Valdiviezo-Mijangos, Jetzabeth Ram\'{i}rez-Sabag, Manuel Coronado A new application for genetic algorithms and direct search optimization methods for solve the inverse problem in tracers test in oil reservoirs is presented in this work. A hybrid method is used to attain a better fit for tracer response curves in producer well with data got from field tests. As it is well known, the tracer tests are used to determinate system rock-fluid properties which are found by nonlinear regression. The properties can be porosity, dispersion coefficient, fracture width, etc. Until now direct search methods have been utilized, which have the inconvenience that they required close initial value of parameters to be optimized to begin iterations. In many practical cases, it is not possible account with this information due at the complexity of the reservoir. Here, we presented a hybrid method which consists on: first use an algorithm genetic which does need any starting point to get the optimal, then we use direct search methods with this initial value for each parameter. We use field data with a mathematical model that describe the flux of tracer between wells and we get excellent results. [Preview Abstract] |
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